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Homesubstructure

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# substructure

Let $\Sigma$ be a fixed signature, and $\mathfrak{A}$ and $\mathfrak{B}$ structures for $\Sigma$. We say $\mathfrak{A}$ is a *substructure* of $\mathfrak{B}$, denoted $\mathfrak{A}\subseteq\mathfrak{B}$, if for all $x\in\mathfrak{A}$ we have $x\in\mathfrak{B}$, and the inclusion map $i\colon\mathfrak{A}\to\mathfrak{B}:x\mapsto x$ is an embedding.

When $\mathfrak{A}$ is a substructure of $\mathfrak{B}$, we also say that $\mathfrak{B}$ is an *extension* of $\mathfrak{A}$.

Defines:

extension

Related:

StructuresAndSatisfaction

Synonym:

submodel

Type of Math Object:

Definition

Major Section:

Reference

## Mathematics Subject Classification

03C07*no label found*

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